Hiroshima University Syllabus

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Academic Year 2023Year School/Graduate School School of Science
Lecture Code HB050000 Subject Classification Specialized Education
Subject Name 代数学B演習
Subject Name
Subject Name in
Exercises in Algebra B
シマダ イチロウ,イイジマ ユウ
Campus Higashi-Hiroshima Semester/Term 3rd-Year,  Second Semester,  4Term
Days, Periods, and Classrooms (4T) Tues3-4,Thur7-8:SCI B305
Lesson Style Seminar Lesson Style
(More Details)
Solve problems, and give presentations on the solutions with the blackboard. Depending on the situation, classes might be held online.  
Credits 2.0 Class Hours/Week   Language of Instruction J : Japanese
Course Level 3 : Undergraduate High-Intermediate
Course Area(Area) 25 : Science and Technology
Course Area(Discipline) 01 : Mathematics/Statistics
Eligible Students
Keywords Field, Galois theory, polynomial equation, geometric problems 
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
(Applicable only to targeted subjects for undergraduate students)
Learn Galois theory, which is one of basic theories in today's mathematics, and its application to classical or concrete problems, by solving problems.  
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
(Abilities and Skills)
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions. 
Class Objectives
/Class Outline
Solve problems on Galois theory and its applications, according to Algebra B.  
Class Schedule According to Algebra B, solve problems about the subjects below.

lesson1 Algebraic equations and Galois theory, field theory
lesson2 Rings and fields, 1
lesson3 Rings and fields, 2
lesson4 Polynomial ring over a field, 1
lesson5 Polynomial ring over a field, 2
lesson6 Field extensions
lesson7 Characteristic, finite fields
lesson8 Irreducibility criteria for polynomials
lesson9 Summary, 1
lesson10 Galois extension and Galois group
lesson11 Examples of Galois group and Galois correspondence
lesson12 Galois groups and algebraic equations
lesson13 Proof of fundamental theorems
lesson14 Summary, 2
lesson15 Geometric problems and Galois theory, field theory

There might be quizzes and report assignments. There is a possibility of having mid-term and final exams jointly with Algebra B. Detailed explanation will be given in the class.

The contents and schedule might change.  
Announced in the class.  
PC or AV used in
(More Details) handouts, blackboard 
Learning techniques to be incorporated  
Suggestions on
Preparation and
Please participate actively. Read all problems and try to give answers. Examine other students' answers.  
Requirements It is recommended that you take Algebra B.  
Grading Method Marks will be based on presentations, reports, quizzes, and exams(if any).  
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching. 
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